%0 Journal Article
%T Lyapunov functionals for the heat equation and sharp inequalities
%A Giuseppe Toscani
%J Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali
%D 2013
%I Accademia Peloritana dei Pericolanti
%R 10.1478/aapp.91s1a18
%X The heat equation represents a powerful instrument to obtain a number of mathematical inequalities in sharp form. This may be not so well-known property goes back more or less to half a century ago, when independently from each others, researchers from information theory [22, 6] and kinetic theory [20] established a useful connection between Boltzmann¡¯s H-functional and Fisher information exactly by means of the solution to the heat equation. In this note, we briefly discuss these original ideas, together with some new application.
%U http://dx.doi.org/10.1478/AAPP.91S1A18